A line segment or ray that is perpendicular to the segment at its midpoint is called

The width of the rectangle is 4.5 meters, and the length is 6 meters.

Let's denote the width of the rectangle as [tex]\( w \)[/tex] and the length as [tex]\( l \)[/tex].

1. The area [tex]\( A \)[/tex] of a rectangle is given by the product of its length and width, so we have the equation:

[tex]\[ A = l \times w \][/tex]

Since the area is given to be 27 square meters, we can write:

[tex]\[ l \times w = 27 \][/tex]

2. The length of the rectangle is 3 meters less than twice the width.

This relationship can be expressed as:

[tex]\[ l = 2w - 3 \][/tex]

This is our second equation.

Now we have a system of two equations with two variables:

[tex]\[ \begin{cases} l \times w = 27 \\ l = 2w - 3 \end{cases} \][/tex]

We can substitute the expression for [tex]\( l \)[/tex] from the second equation into the first equation:

[tex]\[ (2w - 3) \times w = 27 \][/tex]

Expanding the equation, we get:

[tex]\[ 2w^2 - 3w - 27 = 0 \][/tex]

To solve this quadratic equation, we can factor it:

[tex]\[ (2w - 9)(w + 3) = 0 \][/tex]

Setting each factor equal to zero gives us two possible solutions for [tex]\( w \)[/tex]:

[tex]\[ 2w - 9 = 0 \quad \text{or} \quad w + 3 = 0 \][/tex]

Solving for [tex]\( w \)[/tex], we get:

[tex]\[ w = \frac{9}{2} \quad \text{or} \quad w = -3 \][/tex]

Since the width of a rectangle cannot be negative, we discard [tex]\( w = -3 \)[/tex].

Thus, [tex]\( w = \frac{9}{2} \)[/tex] meters, which simplifies to [tex]\( w = 4.5 \)[/tex] meters.

Now we can find the length [tex]\( l \)[/tex] by substituting [tex]\( w = 4.5 \)[/tex] into the second equation:

[tex]\[ l = 2(4.5) - 3 \][/tex]

[tex]\[ l = 9 - 3 \][/tex]

[tex]\[ l = 6 \][/tex]

Answer:

System of equation: 0.75(x+y)=120 and x-y=120

A is correct

Step-by-step explanation:

An aircraft travels with the wind for 120 miles in 0.75 of an hour.

The return trip is flown against the wind and takes exactly 1 hour.

Let speed of aircraft be x mph and speed of wind y mph

Formula:

[tex]speed=\dfrac{Distance}{Time}[/tex]

Case 1: When aircraft along with wind

Speed = x+y

Time = 0.75

Distance = 120

[tex]x+y=\dfrac{120}{0.75}[/tex]

[tex]0.75(x+y)=120[/tex]

0.75(x+y)=120

Case 2: When aircraft against with wind

Speed = x-y

Time = 1

Distance = 120

[tex]x-y=\dfrac{120}{1}=120[/tex]

x-y=120

Hence, The system of equation are 0.75(x+y)=120 and x-y=120

The rate of using water per minute will be 8.5 gallons per minute.

The rate of flow of water is defined as the amount of water or any liquid flowing in a unit of time. If the gallons of water are flowing in some minutes the rate will be measured in the gallons of water.

Given that Kim learned in her science class that every 2 minutes she spends in the shower, she uses 17 gallons of water.

The rate of flow of water will be calculated as:-

Rate of flow = Volume of water / Time

Rate of flow = 17 / 2

Rate of flow = 8.5 gallons per minute

Therefore, the rate of using water per minute will be 8.5 gallons per minute.

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-6 ,4 but speed can't go negative so the answer would be 4.

Answer:

B.

Step-by-step explanation:

when trying to calculate the volume when being given the M or the mass, and the D or density, hears is the calculations needed for that: P=M/V, which also means volume is the mass divided by the volume, or density. Hence, the answer would be mass divided by density. hope this helps!!! (also, please give me brainliest.)

Volume is calculated given mass and density is Mass divided by density.

Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic meter and liter) or by various imperial units (such as the gallon, quart, cubic inch).

Mass is the quantity of matter in a physical body. It is also a measure of the body's inertia, the resistance to acceleration (change of velocity) when a net force is applied.

Density is defined as a measure of how compact the mass in a substance or object is.

Since, density of a substance is measure as the ratio of its mass to its volume,

Density =  Mass/Volume

or, Density x volume =  mass

or, Volume =  Mass/Density

Hence,Volume is calculated given mass and density is Mass divided by density.

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The greatest possible number of club members that we can divide 48 classical CDs and 42 show tune CDs is 6.

HCF is the highest common number or factor that divides two or more than two given numbers completely.

These types of questions can be solved by the concept of HCF.

Given that the glee club has a set of 48 classical CDs and a set of 42 show tune CDs and we have to determine the highest number of club members so that we can distribute these two types of CDs to the club members equally.

∴ The HCF of 42 and 48 is 6, we know 2 and 3 also divides 42 and 48 but they are not the largest number.

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Given two lines are parallel, their slopes are equal. After calculating the slopes of the two lines and solving the equation, we find that the value of 'k' in the question is 4.

In the realm of Mathematics, when two lines are parallel, their slopes are equal. The line y = x + 1 has a slope of 1. To find the slope of the line through (−7,−2) and (−1, k), use the formula for slope, which is m = (y2 - y1) / (x2 - x1). Here, (x1,y1) is (−7,−2) and (x2,y2) is (−1, k). Hence, the equation for slope would look like this: m = (k - (-2)) / (-1 - (-7)).

As the slopes are equal, we can form an equation 1 = (k + 2) / 6. Solving this equation will give us the value of k. By multiplying both sides by 6, we obtain 6 = k + 2. Consequently, subtracting 2 from both sides, we get k = 4.

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We do not square the deviations when calculating the average deviation, because the sum of all deviation scores around the mean equals zero.

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

The average deviation is calculated by taking the absolute value of the deviations from the mean, summing them, and then dividing by the total number of observations.

This gives us a measure of the average distance between each observation and the mean.

The formula for the average deviation is:

average deviation = Σ |x - mean| / n

where x is an observation, mean is the mean of the observations, and n is the total number of observations.

By taking the absolute value of the deviations, we ensure that negative and positive deviations do not cancel each other out when we sum them.

Thus,

We do not square the deviations when calculating the average deviation, because the sum of all deviation scores around the mean equals zero.

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The form used  to write the equation of a line if you knew the slope and x-intercept y=mx−k/m

The slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it

According to the given situation we have given :a slope of 'm' and an x-intercept of 'k'

we can write

y=mx−k/m

and generally, To find the x-intercept, set y = 0 and solve for x.

For example,

Let k be some constant such that

y=mx + k

where

m is the slope.

m=3/4 and the x-intercept is 4

If the x-intercept is 4 this means that x=4 when y=0

So equation:

y=mx + k becomes

0=3/4+ k

k=−3

and our equation is

y=3/4x−3

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An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The value of x is 72.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Let the integer be x and y.

An integer x is divided by an integer y, and the quotient is 24.

This can be written as:

x ÷ y
x/y = 24

x = 24y _____(1)

Now,

The sum of the integer is 75.

x + y = 75

From (1) we get,

24y + y = 75

25y = 75

Divide both sides by 25.

y = 3

Now,

From (2 ) we get,

x + y = 75

x + 3 = 75

Subtracting 3 on both sides.

x = 75 - 3

x = 72

We can also cross-check:

x = 72 and y = 3

= x ÷ y

= 72/3

= 24

Thus,

The value of x is 72.

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For an expression equivalent to, let's say, -8, you could do: -2 + -6.

Answer:

No. The expected value can be a value different from the exact value of x.

Answer:

A

Step-by-step explanation:

BIG BRAIN

Answer:

Samuel's friends have a total of 12 pets.

Explanation:

To find the total number of pets Samuel's friends have, we simply add up the number of each type of pet:

Number of Cats: 5

Number of Dogs: 3

Number of Rabbits: 1

Number of Guinea Pigs: 3

Total number of pets = 5 (cats) + 3 (dogs) + 1 (rabbits) + 3 (guinea pigs) = 12

So, Samuel's friends have a total of 12 pets.

Answer:

y - 9 = 22(x - 3)

Step-by-step explanation:

Answer:

12 square unit.

Step-by-step explanation:

Since, the area of a triangle having vertices [tex](x_1, y_1)[/tex], [tex](x_2, y_2)[/tex] and [tex](x_3, y_3)[/tex] is,

[tex]A=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]

Here, the vertices of the triangle are (0, −2), ​(8, −2) and ​ (9, 1),

Hence, area of the given triangle is,

[tex]A=\frac{1}{2}|0(-2-1)+8(1+2)+9(-2+2)|[/tex]

[tex]=\frac{1}{2}| 0+24+0|[/tex]

[tex]=\frac{24}{2}[/tex]

[tex]=12\text{ square unit}[/tex]

(f + g) (x)= -3 x+ 5

(f + g)(x) = -3x + 5

For given question,

We have been given two functions.

f(x) = x+8 and g(x) = -4x - 3

We need to find the value of (f + g)(x)

This means, we need to find the addition of functions f(x) and g(x)

⇒ (f + g)(x) = f(x) + g(x)

⇒ (f + g)(x) = (x + 8) + (-4x - 3)

⇒ (f + g)(x) = x - 4x + 8 -3

⇒ (f + g)(x) = -3x + 5

Therefore, (f + g)(x) = -3x + 5

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New Orleans has the lower elevation at -8 feet compared to Long Beach, which is at -7 feet, since a lower numerical value below zero indicates a further drop below sea level.

To determine which city has the lower elevation, we need to compare the elevations of Long Beach, California and New Orleans, Louisiana. A lower elevation means that it is further below sea level. Long Beach is at an elevation of -7 feet, while New Orleans is at 8 feet below sea level. In numerical terms, New Orleans’ elevation can be considered as -8 feet because the word 'below' indicates a negative elevation.

Comparing the two elevations:

Long Beach, California: -7 feet

New Orleans, Louisiana: -8 feet

Since -8 is less than -7, we determine that New Orleans has the lower elevation compared to Long Beach.

To solve the inequality -8x - 10 > 7x + 20, combine like terms, isolate the variable term, and solve for x. The correct answer is D) x < -2.

We need to solve the inequality -8x - 10 > 7x + 20.

Therefore, option D.) x < -2 is the correct answer.

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